Another simple and well-known (see e.g.,  [1]}) observation,
which is very helpful in our setting, is the use of list decoding
algorithms for unique decoding.
For a code with distance \(1/2 - \varepsilon /2\) , unique decoding can be obtained by
list decoding at a much smaller error radius of (say) \(1/2 - 1/8\) .
This permits a much more efficient application
of the framework from [2]}, with a milder
dependence on the expansion of the graphs \(G\)  and \(H\) 
in Ta-Shma's construction, resulting in higher rates.
We give a more detailed overview of our approach in sec:strategy.
